Static and dynamic post-buckling analyses of irregularly constrained beams under the small and large deformation assumptions

Abstract

Post-buckling phenomenon has been performing advantages in many applications. In particular, buckling snap-through of slender beams under lateral constraints is of great research interest since low-rate and low-frequency excitations can be transformed into high-rate motions. Electrical energy can be generated from ambient energies through the process. Efficient conversion of the energy phases requires sufficient control over post-buckling response. However, inadequate studies have been conducted to investigate the influence of different lateral constraints on buckling mode transitions. This study aims at developing static and dynamic theoretical models to capture buckling snap-though of slender beams subjected to irregularly bilateral constraints. The models are created based on small and large deformations assumptions, respectively. An algorithm is introduced to discretize the irregular constraints into a gap vector. The equilibrium equations in the presented models are solved using an energy method that minimizes the total energy in the gap vector with respect to the weight coefficient (C m ) of different buckling modes. Experiments were carried out to validate the theoretical results. Good agreements were observed. The proposed models are then used to investigate the effects of the linearly and sinusoidally varied constraints on the beams' post-buckling response. It is found that the deformed shapes of the beams meet the patterns of the constraints. Both the static and dynamic large deformation models are able to measure the end-shortenings that result in severe rotation of the beams' neutral axes. Significant shifting is observed between the deflected beam shapes solved by the static and dynamic models. The presented models are effective in understanding and predicting the static and dynamic post-buckling responses of irregularly constrained beams under small and large deformation assumptions.

Thermally Drawn Highly Conductive Fibers with Controlled Elasticity

“…During the relaxation of the fiber with an integrated electrode, jumps in force correspond to the formation of new buckles (Figure 2b), a behavior characteristic of beam buckling under lateral constraints. [ 48–50 ] These jumps in force are more pronounced in fibers containing higher modulus tungsten electrodes, but are also observed in copper electrodes (Figure S4, Supporting Information). We find that the buckles form in successive steps, as described extensively in literature on planar constrained buckling [ 48–51 ] (Figure 2e; Video S3, Supporting Information).…”

“…[ 48–50 ] These jumps in force are more pronounced in fibers containing higher modulus tungsten electrodes, but are also observed in copper electrodes (Figure S4, Supporting Information). We find that the buckles form in successive steps, as described extensively in literature on planar constrained buckling [ 48–51 ] (Figure 2e; Video S3, Supporting Information). Upon increasing compressive strain, a straight wire buckles into the first mode.…”

Theory, Method and Practice of Metal Deformation Instability: A Review

“…For example, local buckling, global buckling and interactive buckling modes can possibly occur under combing load conditions (as shown in Figure 12 a) [ 155 ]. Jiao et al [ 156 , 157 ] studied the buckling process of hollow microstructure beams by numerical simulation, and according to Figure 12 b, a significant local buckling can be observed. According to the established dynamic and static theoretical models, the buckling fracture of slender beams constrained by irregular sides can be analyzed.…”

An energy harvesting and damage sensing solution based on postbuckling response of nonuniform cross‐section beams

“…Using small deformation assumptions, an energy‐based theoretical model has been developed . The model accurately predicts the postbuckling response of bilaterally constrained uniform cross‐section beams subjected to gradually increasing axial forces.…”

“…Using small deformation assumptions, an energy-based theoretical model has been developed. [35][36][37][38] The model accurately predicts the postbuckling response of bilaterally constrained uniform cross-section beams subjected to gradually increasing axial forces. However, uniform beams do not permit to adequately control the postbuckling behavior and hence optimize the energy conversion efficiency of the system.…”